 Functional-group conversion in step growth

In a balanced bifunctional feed there are initially $N_0$ $A$ groups and $N_0$ $B$ groups. Define the functional-group conversion in step growth by $p=J/N_0$: the reacted fraction of either group type. Each join consumes one of each. Therefore $N=N_0(1-p)$. In the eight-$AB$ example, three joins give $p=3/8$ and four give $p=1/2$. In the latter state only three of eight starting monomer molecules remain isolated: their disappearance fraction is $5/8$, different from $p=1/2$. Neither this group-based $p$ nor disappearance of isolated monomers is the incorporated-feed fraction in the ideal living polymerization count.

With unequal initial counts $A_0\le B_0$, this article always uses $p=J/A_0$, the conversion of the limiting $A$ groups. The reacted fraction of $B$ groups is $J/B_0=rp$, where $r=A_0/B_0$. The fraction of all initial functional groups consumed is $2J/(A_0+B_0)=2rp/(1+r)$. At nonzero conversion these three fractions coincide only at $r=1$. Naming the measured group type prevents an apparently correct equation from using the wrong conversion.